Targeted rectangular conditioning

ABSTRACT

A vectoring controller for configuring a vectoring processor that jointly processes DMT communication signals to be transmitted over, or received from, a plurality of N subscriber lines according to a vectoring matrix. In accordance with an embodiment, the vectoring controller is configured, for given ones of a plurality of tones, to enable the given tone for direct data communication over a first set of N−Mk targeted lines out of the plurality of N subscriber lines, and to disable the given tone for direct data communication over a second disjoint set of Mk supporting lines out of the plurality of N subscriber lines, Mk denoting a non-null positive integer. The vectoring controller is further configured to configure the vectoring matrix to use an available transmit or receive power at the given tone over the second set of Mk supporting lines for further enhancement of data signal gains at the given tone over the first set of N−Mk targeted lines.

TECHNICAL FIELD OF THE INVENTION

The present invention relates to crosstalk mitigation within a wiredcommunication system.

TECHNICAL BACKGROUND OF THE INVENTION

Crosstalk (or inter-channel interference) is a major source of channelimpairment for Multiple Input Multiple Output (MIMO) wired communicationsystems, such as Digital Subscriber Line (DSL) communication systems.

As the demand for higher data rates increases, systems are evolvingtoward higher frequency bands, wherein crosstalk between neighboringtransmission lines (that is to say transmission lines that are in closevicinity over part or whole of their length, such as twisted copperpairs in a cable binder) is more pronounced (the higher frequency, themore coupling).

Different strategies have been developed to mitigate crosstalk and tomaximize effective throughput, reach and line stability. Thesetechniques are gradually evolving from static or dynamic spectralmanagement techniques to multi-user signal coordination (vectoringhereinafter).

One technique for reducing inter-channel interference is joint signalprecoding: the transmit data symbols are jointly passed through aprecoder before being transmitted over the respective communicationchannels. The precoder is such that the concatenation of the precoderand the communication channels results in little or no inter-channelinterference at the receivers.

A further technique for reducing inter-channel interference is jointsignal postcoding (or post-processing): the receive data symbols arejointly passed through a postcoder before being detected. The postcoderis such that the concatenation of the communication channels and thepostcoder results in little or no inter-channel interference at thedetectors. Postcoders are also sometimes referred to as crosstalkcancellation filters.

Signal vectoring is typically performed at a traffic aggregation pointas vectoring primarily implies that data symbols concurrentlytransmitted over, or received from, the vectored lines are bunched andsynchronously passed all together through the precoder or postcoder. Forinstance, signal vectoring is advantageously performed within a DigitalSubscriber Line Access multiplexer (DSLAM) deployed at a Central office(co), or as a fiber-fed remote unit closer to subscriber premises(street cabinet, pole cabinet, building cabinet, etc). Such a remoteunit may also be referred to as a remote DSLAM, or as a DistributionPoint Unit (DPU). Signal precoding is particularly appropriate fordownstream communication (toward customer premises), while signalpostcoding is particularly appropriate for upstream communication (fromcustomer premises).

The choice of the vectoring group, that is to say the set ofcommunication lines, the signals of which are jointly processed, israther critical for achieving good crosstalk mitigation performances.Within a vectoring group, each communication line is considered as adisturber line inducing crosstalk into the other communication lines ofthe group, and the same communication line is considered as a victimline incurring crosstalk from the other communication lines of thegroup. Crosstalk from lines that do not belong to the vectoring group istreated as alien noise and is not canceled.

Ideally, the vectoring group should match the whole set of communicationlines that physically and noticeably interfere with each other. Yet,local loop unbundling on account of national regulation policies and/orlimited vectoring capabilities may prevent such an exhaustive approach,in which case the vectoring group would only include a sub-set of theinterfering lines, thereby yielding limited vectoring gains.

More formally, an N×N MIMO system can be described by the followinglinear model:

y _(k) =H _(k) x _(k) +z _(k)  (1),

wherein the N-component complex vector x_(k), respectively y_(k), is adiscrete frequency representation, as a function of thefrequency/carrier/tone index k, of the symbols transmitted over,respectively received from, the N vectored channels,wherein the N×N complex matrix H_(k) is the channel matrix: the (i,j)-thcomponent Hu of the channel matrix H_(k) describes how the communicationsystem produces a signal on the i-th channel output in response to asignal being fed to the j-th channel input; the diagonal elements of thechannel matrix describe direct channel coupling, and the off-diagonalelements of the channel matrix (also referred to as the crosstalkcoefficients) describe inter-channel coupling,and wherein the N-component complex vector z_(k) denotes additive noiseover the N channels, such as Radio Frequency Interference (RFI) orthermal noise.

Linear signal precoding and postcoding are advantageously implemented bymeans of matrix products.

In downstream, the linear precoder performs a matrix-product in thefrequency domain of a transmit vector u_(k) with a precoding matrixP_(k) before actual transmission over the respective subscriber lines,i.e. actual transmit vector is x_(k)=P_(k)u_(k) in eq. (1), theprecoding matrix P_(k) being such that the overall channel matrixH_(k)P_(k) is diagonalized, meaning the off-diagonal coefficients of theoverall channel H_(k)P_(k), and thus the inter-channel interference,mostly reduce to zero.

Practically, and as a first order approximation, the precodersuperimposes anti-phase crosstalk pre-compensation signals over thevictim line along with the direct signal that destructively interfere atthe receiver with the actual crosstalk signals from the respectivedisturber lines.

In upstream, the linear postcoder performs a matrix-product in thefrequency domain of the receive vector y_(k) with a postcoding matrixQ_(k) to recover the transmit vector u_(k) (after channel equalizationand power normalization), i.e. detection is performed ony′_(k)=Q_(k)y_(k), the postcoding matrix Q_(k) being such that theoverall channel matrix Q_(k)H_(k) is diagonalized, meaning theoff-diagonal coefficients of the overall channel Q_(k)H_(k), and thusthe inter-channel interference, mostly reduce to zero.

The performance of signal vectoring depends critically on the componentvalues of the precoding and postcoding matrix, which component valuesare to be computed and updated according to the actual and varyingchannel couplings.

The various channel couplings are estimated by a vectoring controllerbased on pilot (or probing) signals transmitted over the respectivechannels. The pilot signals are typically transmitted during dedicatedtime periods and/or over dedicated tones.

For instance, in the recommendation entitled “Self-FEXT Cancellation(Vectoring) For Use with VDSL2 Transceivers”, ref. G.993.5 (VectoredVDSL2 hereinafter), and adopted by the International TelecommunicationUnion (ITU) in April 2010, the transceiver units send pilot signals onthe so-called SYNC symbols. The SYNC symbols occur periodically afterevery super frame, and are transmitted synchronously over all thevectored lines (super frame alignment). A similar technique has beenadopted in 6.9701 ITU recommendation (G.fast hereinafter).

On a given disturber line, a subset of the tones of a SYNC symbol (pilottones hereinafter) are all 4-QAM modulated by the same pilot digit froma given pilot sequence, and transmit one of two complex constellationpoints, either ‘1+j’ corresponding to ‘+1’ or ‘−1−j’ corresponding to‘−1’ (Vectored VDSL2); or transmit one of three complex constellationpoints, either ‘1+j’ corresponding to ‘+1’ or ‘−1−j’ corresponding to‘−1’ or ‘0+0j’ corresponding to ‘0’ (G.fast).

On a given victim line, both the real and imaginary part of the receivedfrequency sample before equalization (G.fast), or of the normalizedslicer error, which is the difference vector between the received andproperly equalized frequency sample and the constellation point ontowhich this frequency sample is demapped (Vectored VDSL2 and G.fast), aremeasured on a per pilot tone basis and reported to the vectoringcontroller for estimation of the various channel couplings.

The successive error samples gathered over a given victim line are nextcorrelated with the pilot sequence used over a given disturber line inorder to obtain an estimate of the channel coupling from the givendisturber line into the given victim line. To reject the crosstalkcontributions from the other disturber lines, the pilot sequences usedover the respective disturber lines are mutually orthogonal (e.g.,Walsh-Hadamard sequences).

The crosstalk estimates are eventually used for initializing or updatingthe coefficients of the precoding or postcoding matrix, typically bymeans of a first or higher-order matrix inversion of the channel matrix(e.g., zero-forcing precoder) or by means of an iterative update (e.g.,LMS precoder).

With the advent of new copper access technologies and the use of evenbroader spectrum up to and beyond 100 MHz, the crosstalk couplingsubstantially increases. Consequently, the superimposition of thecrosstalk precompensation signals on a victim line may cause a violationof the transmit Power Spectral Density (PSD) mask, which defines theallowed amount of signal power for an individual user as a function offrequency, and may also result in signal clipping within the Digital toAnalog Converter (DAC) causing severe signal distortions.

A first solution is to scale down the gains of the direct signals, andthus of the corresponding precompensation signals, such that thetransmit signals, including both the direct and precompensation signals,remain within the allowed transmit power bounds. The PSD reduction isline and frequency dependent, and may change over time, e.g. when a linejoins or leaves the vectoring group. The change in direct signal gainsmust be communicated to the respective receivers for proper channelequalization.

A second solution is the use of Non-Linear Precoding (NLP), whichapplies modulo arithmetic operation to shift a transmit constellationpoint with excessive power back within the constellation boundary. Atthe receiver, the same modulo operation will shift the signal back toits original position. NLP is significantly more computationally complexthan linear precoding. For example, NLP typically require matrixdecompositions, such as QR matrix decomposition, and numerousalternating linear and non-linear operations.

A further and important consequence of the use of such a broad frequencyspectrum is the ill-conditioning of the channel matrix at numeroustones, i.e. the channel matrix is singular or almost singular, andmatrix inversion for achieving zero-forcing condition yields largeprecoder/postcoder coefficients. Thus significant down-scaling needs tobe applied to communication signals for linear precoding, resulting invery poor vectoring gains.

Such channel singularities also cause very large fluctuations of theprecoder/postcoder coefficients across frequency, meaning that morememory is required to represent the coefficients numerically, whichdirectly translates into higher costs for the vectoring processor.

Last, channel ill-conditioning yields a large distribution of data ratesand aggregate transmit power across the subscriber loops. Even withequal loop lengths, we see that the data rate distribution can vary morethan 50% from line to line. This is problematic for operators, who aretypically interested in delivering common guaranteed data rates (inservice classes) to the end-users.

A technique known as tone suppression can circumvent the channelill-conditioning: if, on a particular tone, the N×N channel matrix of anN-users system is ill-conditioned (i.e., has a large condition number),then one looks for a subset of N−M users such that the corresponding(N−M)×(N−M) reduced channel matrix is well-conditioned (i.e., has a lowcondition number). The M suppressed lines do not carry any directcommunication signal over this tone (i.e., transmit gain and bit loadingare both set to zero). An (N−M)×(N−M) precoder/postcoder is then used tocancel the crosstalk between the N−M remaining users. Tone suppressionallows the N−M users to still get good data rates at the expense of theM suppressed users. The set of suppressed lines, and the number ofsuppressed lines M, may be different across tones. By appropriatelyselecting which lines to suppress on which tone, the overall data ratecan be improved relative to a system that uses full N×N inverseprecoding/postcoding on every tone.

SUMMARY OF THE INVENTION

It is an object of the present invention to further improve thevectoring gains in the event of the communication channel beingill-conditioned.

In accordance with a first aspect of the invention, a vectoringcontroller for configuring a vectoring processor that jointly processesDiscrete Multi-Tone (DMT) communication signals to be transmitted over,or received from, a plurality of N subscriber lines according to avectoring matrix is adapted, for given ones of a plurality of tones, toenable the given tone for direct data communication over a first set ofN−M_(k) targeted lines out of the plurality of N subscriber lines, andto disable the given tone for direct data communication over a seconddisjoint set of M_(k) supporting lines out of the plurality of Nsubscriber lines, M_(k) denoting a non-null positive integer. Thevectoring controller is further adapted to configure the vectoringmatrix to use an available transmit or receive power at the given toneover the second set of M_(k) supporting lines for further enhancement ofdata signal gains at the given tone over the first set of N−M_(k)targeted lines.

In one embodiment of the invention, the configured vectoring matrix is arectangular N×(N−M_(k)) precoding matrix with at least one non-nulloff-diagonal precoding coefficient for the respective M matrix rowscorresponding to the second set of M_(k) supporting lines.

In a further embodiment of the invention, the configured rectangularvectoring matrix is a generalized inverse matrix of a (N−M_(k))×Nreduced channel matrix comprising far-end coupling coefficients from theplurality of N subscriber lines into the first set of N−M_(k) targetedlines.

In still a further embodiment of the invention, the generalized inversematrix is a Moore-Penrose pseudo-inverse of the (N−M_(k))×N reducedchannel matrix.

In one embodiment of the invention, the configured vectoring matrix is arectangular (N−M_(k))×N postcoding matrix with at least one non-nulloff-diagonal postcoding coefficient for the respective M matrix columnscorresponding to the second set of M_(k) supporting lines.

In a further embodiment of the invention, the configured rectangularvectoring matrix is a generalized inverse matrix of a N×(N−M_(k))reduced channel matrix comprising far-end coupling coefficients from thefirst set of N−M_(k) targeted lines into the plurality of N subscriberlines.

In still a further embodiment of the invention, the generalized inversematrix is a Moore-Penrose pseudo-inverse of the N×(N−M_(k)) reducedchannel matrix.

In one embodiment of the invention, the vectoring controller is furtheradapted to determine the first and second sets of lines on a per tonebasis.

In one embodiment of the invention, the plurality of tones comprisesill-conditioned tones.

In one embodiment of the invention, the vectoring controller is furtheradapted to update respective line metrics currently achieved over theplurality of N subscriber lines given the so-enabled and so-disabledtones and the so-configured vectoring matrices while iterating throughthe plurality of tones, and to determine the first and second sets oflines based on the so-updated line metrics.

In a further embodiment, the vectoring controller is further adapted toassign at least one subscriber line of the plurality of N subscriberlines, whose updated line metric exceeds a given line metric target, tothe second set of M_(k) supporting lines for at least one subsequenttone iteration.

Alternatively, the vectoring controller is further adapted to assign atleast one subscriber line of the plurality of N subscriber lines, whoseupdated line metric exceeds by a given margin at least one updated linemetric of at least one further subscriber line of the plurality of Nsubscriber lines, to the second set of M_(k) supporting lines for atleast one subsequent tone iteration.

The line metrics may refer to respective aggregate data rates and/oraggregate transmit powers achieved so far over the plurality of Nsubscriber lines given the so-enabled and so-disabled tones and the soconfigured vectoring matrices.

Such a vectoring controller typically forms part of an access nodeproviding broadband communication services to subscribers over a copperplant and deployed at a co or at a remote location closer to subscriberpremises, such as a DSLAM or a DPU.

In accordance with another aspect of the invention, a method forconfiguring a vectoring processor that jointly processes DMTcommunication signals to be transmitted over, or received from, aplurality of N subscriber lines according to a vectoring matrixcomprises, for given ones of a plurality of tones, enabling the giventone for direct data communication over a first set of N−M_(k) targetedlines out of the plurality of N subscriber lines, and disabling thegiven tone for direct data communication over a second disjoint set ofM_(k) supporting lines out of the plurality of N subscriber lines, M_(k)denoting a non-null positive integer. The method further comprisesconfiguring the vectoring matrix to use an available transmit or receivepower at the given tone over the second set of M_(k) supporting linesfor further enhancement of data signal gains at the given tone over thefirst set of N−M_(k) targeted lines.

Embodiments of a method according to the invention correspond with theembodiments of a vectoring controller according to the invention.

The present invention proposes to boost the data signal gains at a giventone over N−M_(k) targeted lines (i.e., targeted for direct datacommunication) by using the transmit power (precoding) or receive power(postcoding) that has been made available over M_(k) supporting lines(i.e., supporting data communication to the targeted set) on account ofno direct data communication taking place over the M_(k) supportinglines at that given tone.

In this approach, we improve channel conditioning by eliminating certainrows (precoding) or certain columns (postcoding) of the channel matrix,rather than by eliminating both rows and columns. This results in arectangular (N−M_(k))×N (precoding) or N×(N−M_(k)) (postcoding) reducedchannel matrix compared to the known square (N−M_(k))×(N−M_(k)) reducedchannel matrix when the suppressed lines are entirely ignored.Physically, this means that even when the number of users providing datais less than N, namely N−M_(k), the precoder still generates N outputsignals that are transmitted on all N vectored lines, and likewise thepostcoder still relies on N input signals received from all N vectoredlines.

For instance, suppose that we have an ill-conditioned system of N=10lines that is better conditioned when line 10 is not targeted for directdata communication.

When precoding the full system, the signal sent on line 10 uses some ofits power budget to send data intended for receiver 10, and some of itsbudget to cancel crosstalk coming from lines 1 to 9. With the knownsquare tone suppression, no signal at all is sent on line 10. Receiver10 gets no data, but lines 1 to 9 are relieved from having to use any oftheir power budget to cancel crosstalk from line 10. With the proposedrectangular conditioning, the full power budget of line 10 is dedicatedto sending data intended for lines 1 to 9. Lines 1 to 9 are relievedfrom having to cancel crosstalk from line 10, and moreover they benefitfrom this additional transmit power used in their behalf.

When postcoding the full system, the signal received on line 10 is usedto remove, from the received signals on lines 1 to 9, crosstalkoriginating from line 10. In doing so, some received noise on line 10 isintroduced into lines 1 to 9. With the known square tone suppression, nosignal is sent on line 10. Receiver 10 gets no data, but lines 1 to 9are relieved from having to remove crosstalk from line 10, and hence arenot affected by noise received on line 10. With the proposed rectangularconditioning, the received signal on line 10, which contains crosstalksignals received from lines 1 to 9, may be applied to aiding thereception of data from lines 1 to 9. Lines 1 to 9 are relieved fromhaving to cancel crosstalk from line 10, and moreover they benefit fromadditional received power from line 10 used in their behalf.

To take full advantage of this rectangular channel, we use awell-designed rectangular N×(N−M_(k)) precoder or (N−M_(k))×N postcoderfor coherent combining of the N−M_(k) data communication signalstraveling through the different propagation paths (inc. the direct andindirect propagation paths) at the N−M_(k) receivers (precoding) ordetectors (postcoding) coupled to the N−M_(k) targeted lines. Owing tothis coherent combining, the power of the useful receive signal (i.e.,the data signal) is substantially increased over the N−M_(k) targetedlines before signal detection, and so is their Signal to Noise Ratio(SNR) and thus their achievable data rate.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other objects and features of the invention will becomemore apparent and the invention itself will be best understood byreferring to the following description of an embodiment taken inconjunction with the accompanying drawings wherein:

FIG. 1 represents an overview of an access plant;

FIG. 2 represents further details about an access node;

FIG. 3 represents an overview of rectangular precoding as per thepresent invention;

FIG. 4 represents an overview of rectangular postcoding as per thepresent invention;

FIG. 5 represents a method flow chart for determining the sets oftargeted and supporting lines for successive tones; and

FIGS. 6A, 6B and 6C represent various performance plots for rectangularconditioning versus known techniques (full inverse and square tonesuppression).

DETAILED DESCRIPTION OF THE INVENTION

The square brackets hereinafter surround terms that are deemed to beoptional, and thus an expression such as e.g. “the [normalized] channelmatrix” shall be construed as either “the channel matrix” or “thenormalized channel matrix”.

There is seen in FIG. 1 an access plant 1 comprising a network unit 10at a C0, an access node 20 coupled via one or more optical fibers to thenetwork unit 10, and further coupled via a copper plant to CustomerPremises Equipment (CPE) 30 at various subscriber locations. Thetransmission media of the copper plant is typically composed of copperUnshielded Twisted Pairs (UTP).

As an illustrative example, the copper plant comprises four subscriberlines L₁ to L₄ sharing a common access segment 40, and then goingthrough dedicated loop segments 50 for final connection to CPEs 30 ₁ to30 ₄ respectively.

Within the common access segment 40, the subscriber lines L₁ to L₄ arein close vicinity and thus induce crosstalk into each other (see thearrows in FIG. 1 between the respective subscriber lines).

The access node 20 comprises a Vectoring Processing Unit 21 (or VPU) forjointly processing the data symbols that are being transmitted over, orreceived from, the copper plant in order to mitigate the crosstalk andto increase the achievable data rates.

There is seen in FIG. 2 further details about an access node 100 andrespective CPEs 200.

The access node 100 comprises:

-   -   transceivers 110;    -   a Vectoring Processing Unit (VPU) 120; and    -   a Vectoring Control Unit (VCU) 130 for controlling the operation        of the VPU 120.

The transceivers 110 are individually coupled to the VPU 120 and to theVCU 130. The VCU 130 is further coupled to the VPU 120.

The transceivers 110 individually comprise:

-   -   a Digital Signal Processor (DSP) 111; and    -   an Analog Front End (AFE) 112.

The transceivers 110 are coupled to respective transceivers 210 withinthe CPEs 200 through respective subscriber lines L₁ to L_(N), which areassumed to form part of the same vectoring group.

The transceivers 210 individually comprise:

-   -   a Digital Signal Processor (DSP) 211; and    -   an Analog Front End (AFE) 212.

The AFEs 112 and 212 individually comprise a Digital-to-Analog Converter(DAC) and an Analog-to-Digital Converter (ADC), a transmit filter and areceive filter for confining the signal energy within the appropriatecommunication frequency bands while rejecting out-of-band interference,a line driver for amplifying the transmit signal and for driving thetransmission line, and a Low Noise Amplifier (LNA) for amplifying thereceive signal with as little noise as possible.

In case of Frequency Division Duplexing (FDD) operation where downstreamand upstream communications operate simultaneously over the sametransmission medium in distinct and non-overlapping frequency bands, theAFEs 112 and 212 further comprise a hybrid for coupling the transmitteroutput to the transmission medium and the transmission medium to thereceiver input while achieving low transmitter-receiver coupling ratio.The AFE may further accommodate echo cancellation filters to reduce thecoupling ratio at a further extent.

In case of Time Duplexing Division (TDD) operation where downstream andupstream communications operate over the same frequency band but indistinct and non-overlapping time slots, the hybrid can beadvantageously omitted as the transmitter and receiver operate inalternate mode: the receive circuitry is switched OFF (or the receivesignal is discarded) while the transmit circuitry is active, and the wayaround, the transmit circuitry is switched OFF while the receivecircuitry is active.

The AFEs 112 and 212 further comprise impedance-matching circuitry foradapting to the characteristic impedance of the transmission medium,clipping circuitry for clipping any voltage or current surge occurringover the transmission medium, and isolation circuitry (typically atransformer) for DC-isolating the transceiver from the transmissionmedium.

The DSPs 111 and 211 are configured to operate downstream and upstreamcommunication channels for conveying user traffic over the subscriberlines L₁ to L_(N).

The DSPs 111 and 211 are further configured to operate downstream andupstream control channels that are used to transport control traffic,such as diagnosis, management or On-Line Reconfiguration (OAR) commandsand responses. Control traffic is multiplexed with user traffic over thetransmission medium.

More specifically, the DSPs 111 and 211 are for encoding and modulatinguser and control data into DMT symbols, and for de-modulating anddecoding user and control data from DMT symbols.

The following transmit steps are typically performed within the DSPs 111and 211:

-   -   data encoding, such as data multiplexing, framing, scrambling,        error correction encoding and interleaving;    -   signal modulation, comprising the steps of ordering the tones        according to a tone ordering table, parsing the encoded bit        stream according to the respective bit loadings of the ordered        tones, and mapping each chunk of bits onto an appropriate        transmit constellation point (with respective carrier amplitude        and phase), possibly with Trellis coding;    -   signal scaling, such as power normalization, transmit PSD        shaping and transmit gain scaling;    -   Inverse Fast Fourier Transform (IFFT);    -   Cyclic Prefix (CP) insertion; and    -   time-windowing.

The following receive steps are typically performed within the DSPs 111and 211:

-   -   time-windowing and CP removal;    -   Fast Fourier Transform (FFT);    -   Frequency EQualization (FEQ);    -   signal de-modulation and detection, comprising the steps of        applying to each and every equalized frequency sample an        appropriate constellation grid, the pattern of which depends on        the respective bit loading, detecting the expected transmit        constellation point and the corresponding transmit bit sequence,        possibly with Trellis decoding, and re-ordering all the detected        chunks of bits according to the tone ordering table; and    -   data decoding, such as data de-interleaving, error correction        decoding, de-scrambling, frame delineation and de-multiplexing.

Some of these transmit or receive steps can be omitted, or someadditional steps can be present, depending on the exact digitalcommunication technology being used.

The DSPs 111 are further configured to supply transmit frequency samplesu_(k) to the VPU 120 before Inverse Fast Fourier Transform (IFFT) forjoint signal precoding, and to supply receive frequency samples y_(k) tothe VPU 120 after Fast Fourier Transform (FFT) for joint signalpost-processing.

The DSPs 111 are further configured to receive pre-compensated transmitsamples x_(k) from the VPU 120 for further transmission, and to receivepost-compensated receive samples y′_(k) from the VPU 120 for furtherdetection. Alternatively, the DSPs 111 may receive correction samples toadd to the initial frequency samples before further transmission ordetection.

The VPU 120 is configured to mitigate the crosstalk induced over thesubscriber lines. The VPU 120 comprises a linear precoder configured tomultiply a vector u_(k) of transmit frequency samples with a precodingmatrix P_(k) in order to pre-compensate an estimate of the expectedcrosstalk, and a linear postcoder configured to multiply a vector ofreceive frequency samples y_(k) with a crosstalk cancellation matrixQ_(k) so as to post-compensate an estimate of the incurred crosstalk.

In the matrix P_(k) or Q_(k), a row i is associated with a particularvictim line L_(i), while a column j is associated with a particulardisturber line L_(j).

The VCU 130 is basically for controlling the operation of the VPU 120,and more specifically for estimating the crosstalk coefficients betweenthe subscriber lines of the vectoring group, and for initializing andupdating the coefficients of the precoding matrix P_(k) and of thecrosstalk cancellation matrix Q_(k) from the so-estimated crosstalkcoefficients.

The VCU 130 starts first by configuring the transceivers 110 and 210with the respective pilot sequences to use for modulation of the pilottones of the pilot symbols (SYNC symbols). The pilot sequences comprisesT pilot digits using {+1, −1} or {+1, 0, −1} as alphabet. The pilotdigit that modulates a given tone k during pilot symbol position t overline L_(i) is denoted as w_(i,k) ^(t). Presently, the pilot symbols arenot processed through the VPU 120 as one needs first to characterize thechannel matrix per se.

The VCU 130 next gathers measurement samples as measured by thetransceivers 110 and 210 while the pilot symbols are being transmitted.The measurement sample as measured by the transceiver 110 i or 210 iover a victim line L_(i) at tone k during pilot symbol position t isdenoted as e_(i,k) ^(t).

The VCU 130 correlates T measurement samples {e_(i,k) ^(t)}_(t=t) ₀_(. . . t) ₀ _(·T−1) as measured over a given victim line L_(i) during acomplete acquisition cycle with the T pilot digits {w_(j,k) ^(t)}_(t=t)₀ _(. . . t) ₀ _(+T−1) of the pilot sequence transmitted over a givendisturber line L_(j) so as to obtain a crosstalk estimate from thedisturber line L_(j) into the victim line L_(i) at frequency index k. Asthe pilot sequences are mutually orthogonal, the contributions from theother disturber lines reduce to zero after this correlation step.

The channel matrix and/or the normalized channel matrix are determinedbased on these correlation results. The nominal channel matrix isderived from a measure of the raw receive signals before equalization,whereas the normalized channel matrix is derived from a measure of theslicer errors after channel equalization.

The so-determined channel matrix may exhibit ill-conditioning atspecific tones, that is to say one or more row(s) and/or column(s) ofthe channel matrix corresponding to one or more subscriber lines can beexpressed as, or come close to, a linear combination of the other rowsor columns, which makes the channel matrix singular or almost singular,and yields very large vectoring coefficients for zero-forcing vectoring.

Typically, the matrix singularity is quantified by means of a conditionnumber, and a matrix is said to be ill-conditioned when that conditionnumber exceeds some given threshold. For instance, the ratio between thelargest and lowest singular values of the channel matrix is a goodindicator for ill-conditioning and can be used as condition number.

The VCU 130 is further configured to characterize the ill-conditioningof the so-determined channel matrix at respective tones, and if thechannel matrix is characterized as being ill-conditioned at a giventone, then the VCU 130 is further configured to select one or more linesand to disable the given tone for direct data communication over theselines so as the corresponding reduced channel matrix iswell-conditioned. The set of lines for which the given tone is keptactive for direct data communication is referred to as the targeted set,whereas the set of lines for which the given tone is disabled for directdata communication is referred to as the supporting set.

The VCU 130 distributes targeted and supporting roles to the varioussubscriber lines L₁ to L_(N) across different tones. Indeed, this ismade possible because, when one matrix row or column is [almost] alinear combination of say two other matrix rows or columns, then any ofthe three subscriber lines corresponding to these three matrix rows orcolumns can be selected for the supporting set in order to‘re-orthogonalize’ the channel matrix and make it no longer singular.Owing to the frequency coherence of the channel, the same three linesare likely to be again in the same linear relationship at neighboringtones, and the VCU 130 can select each of these 3 lines in turn. The VCU130 thus has some degree of freedom for balancing targeted andsupporting roles across the lines and achieving some kind of fairness asit will be set forth further in the description.

Also it is noteworthy that, with TDD, the sets of targeted andsupporting lines for a given tone can be different in upstream anddownstream.

For every line Li, a set of disabled tones ST_(i) is determined and sentto the respective transceiver 110 i (see “ST_(i)={k₁, . . . }” in FIG.2), or to a central communication controller that manages thecommunication parameters of the transceivers 110 and 210. Thereupon, thetransceiver 110 i configures both the bit loadings b_(i,k) and transmitgains r_(i,k) to zero for all tones k in the set ST_(i). The new bitloading and transmit gain values are communicated to the respective peertransceiver 210 i (see “b_(i,k1)=0” and “r_(i,k1)=0” in FIG. 2).

It is noteworthy that pilot signals keep on being transmitted over thesedisabled tones notwithstanding their transmit gain and bit loading,which have been both set to zero. By so doing, the full [normalized]channel matrix can still be estimated on every tone.

Let k be such an ill-conditioned tone: direct data communication at tonek is to be disabled over one or more subscriber lines in order to obtaina well-conditioned reduced channel matrix at tone k.

Let L={L₁, . . . , L_(N)} denote the set of all vectored lines. LetA_(k) denote the set of targeted lines at tone k, that is to say the setof lines for which tone k is kept enabled for direct data communication(i.e., corresponding bit loading and transmit gain are both differentfrom zero), and let Bk denote the set of supporting lines at tone k,that is to say the set of lines for which tone k is disabled for directdata communication (i.e., corresponding bit loading and transmit gainare both set to zero).

We have:

L=A _(k) ∪B _(k) and A _(k) ∩B _(k)=Ø  (2).

Let M_(k) denote the size of the set B_(k), implying that N−M_(k) is thesize of the set A_(k) on account of the set equations (2). The numberM_(k) of lines that need to be removed from the targeted set is mostlydetermined by the condition of the [normalized] channel matrix atrespective tones, but may also depend on further criteria.

Let H_(k) denote the N×N [normalized] channel matrix at tone k, and letus arrange the [normalized] channel matrix as

${H_{k} = \begin{bmatrix}H_{Ak} \\H_{Bk}\end{bmatrix}},$

wherein H_(Ak) denotes a reduced (N−M_(k))×N [normalized] channel matrixcomprising the N−M_(k) rows of the [normalized] channel matrix H_(k)corresponding to the set of targeted lines A_(k) and all N columns, andH_(Bk) denotes a reduced M_(k)×N [normalized] channel matrix comprisingthe M_(k) rows of the [normalized] channel matrix H_(k) corresponding tothe set of supporting lines B_(k) and all N columns. In other words, therows of the [normalized] channel matrix H_(k) have been re-arranged forthe supporting lines B_(k) to occupy the last M_(k) rows. Thisrearrangement of rows and columns is to simplify the notation forexposition, and is not necessary in practice as should be clear to thoseskilled in the art.

Let P_(k)=[P_(Ak) P_(Bk)] denote the precoding matrix used at tone k,with P_(Ak) denoting a reduced N×(N−M_(k)) precoding matrix comprisingthe N−M_(k) columns of the precoding matrix P_(k) corresponding to theset of targeted lines A_(k) and all N rows, and P_(Bk) denoting areduced N×M_(k) precoding matrix comprising the M_(k) columns of theprecoding matrix P_(k) corresponding to the set of supporting linesB_(k) and all N rows.

With zero-forcing precoding and when targeting all lines, we would haveP_(k)=H_(k) ⁻¹.

$\left. \begin{matrix}0 & S_{bk}\end{matrix} \right\rbrack$

be the transmit gain scaling diagonal matrix at tone k for conformanceto a transmit PSD mask and total aggregate power, with S_(Ak) and S_(Bk)being the diagonal matrices corresponding to the set of targeted linesA_(k) and the set of supporting lines B_(k) respectively. The diagonalcoefficients of the diagonal matrix S_(Bk) are set to zero as there areno data communication signals transmitted over the supporting linesB_(k) at tone k.

With this notation in mind, the VCU 130 is further configured, forrespective ones of the ill-configured tones used for downstreamcommunication:

-   -   to determine a set A_(k) of targeted lines and a corresponding        set B_(k) of supporting lines to obtain a well-conditioned        reduced [normalized] channel matrix H_(Ak); and    -   to compute or recompute a rectangular precoding matrix {tilde        over (P)}_(Ak) for the targeted lines A_(k) for which the        following three conditions hold:        -   a) The rows of {tilde over (P)}_(Ak) corresponding to the            supporting lines B_(k) are not forced to zero, and thus            precompensation signals are transmitted over the supporting            lines B_(k).        -   b) The rows of {tilde over (P)}_(Ak) corresponding to the            targeted lines A_(k) are not the same as the corresponding            rows of the full precoding matrix P_(k) (i.e., when all            lines are targeted). This emphasizes that one does not just            take the rows of the inverse of the full [normalized]            channel matrix P_(k)=H_(k) ⁻¹.        -   c) The (re)computed vectoring matrix {tilde over (P)}_(Ak)            has a zero-forcing design and diagonalizes the overall            channel over the targeted lines A_(k):

$\begin{matrix}{{\left. \begin{matrix}{H_{Ak}{\overset{\sim}{P}}_{Ak}S_{Ak}} & {H_{Ak}{\overset{\sim}{P}}_{Ak}S_{Ak}} \\{{{}_{}^{}{}_{}^{}}S_{Ak}} & {H_{Bk}P_{Bk}S_{Bk}}\end{matrix} \right\rbrack = {\begin{bmatrix}{H_{Ak}{\overset{\sim}{P}}_{Ak}S_{Ak}} & 0 \\{H_{Bk}{\overset{\sim}{P}}_{Ak}S_{Ak}} & 0\end{bmatrix} = \begin{bmatrix}D_{Ak} & 0 \\X & 0\end{bmatrix}}},} & (3)\end{matrix}$

-   -   -    with D_(Ak) denoting a diagonal matrix, and X denoting a            ‘don't care’. The coefficients of the precoding matrix            {tilde over (P)}_(Bk) are made irrelevant by setting all            gains of the diagonal matrix S_(Bk) to zero. These            coefficients can be left unchanged, or can be reset to zero            too.

One possible concrete precoder computation is to use the Moore-Penrosepseudo-inverse of the reduced [normalized] channel matrix H_(Ak) asfollows:

{tilde over (P)} _(Ak) =H _(Ak) ^(H)(H _(Ak) H _(Ak) ^(H))⁻¹  (4).

However, this is not the only choice, but a whole family of generalizedinverses can serve as precoder. For instance, the following generalizedinverse could be used as zero-forcing precoder too:

{tilde over (P)} _(Ak) =WH _(Ak) ^(H)(H _(Ak) WH _(Ak) ^(H))⁻¹  (5),

wherein W denotes a N×N diagonal matrix with real diagonal coefficients.

In general, an N×(N−M_(k)) precoder has N(N−M_(k)) degrees of freedom,of which (N−M_(k))² should be used to ensure that all crosstalk iscanceled (D_(A) is diagonal), and the remaining (N−M_(k))M_(k) degreesof freedom are available to try to maximize the power of the receivecommunication signals on the N−M_(k) targeted lines, that is to say tomake diagonal values of the diagonal matrix D_(Ak) as large as possiblewhile meeting the various power constraints.

A few words regarding the use of the channel matrix or the normalizedchannel matrix for the computation of the precoding matrix.

The channel matrix and the normalized channel matrix only differ byleft-multiplication with a diagonal matrix F_(k) comprising the inversesof the diagonal elements of H_(k):

G _(k) =F _(k) H _(k)  (5),

wherein H_(k) and G_(k) denote the now-differentiated channel matrix andnormalized channel matrix respectively.

By virtue of eq. (4) or (5), the corresponding precoding matrices willonly differ by right-multiplication with a diagonal matrix:

{tilde over (P)} _(Ak) =G _(Ak) ^(H)(G _(Ak) G _(Ak) ^(H))⁻¹

=(F _(Ak) H _(Ak))^(H)((F _(Ak) H _(Ak))(F _(Ak) H _(Ak))^(H))⁻¹ =H_(Ak) ^(H) F _(Ak) ^(H)(F _(Ak) H _(Ak) H _(Ak) ^(H) F _(Ak)^(H))⁻¹  (6),

=H _(Ak) ^(H) F _(Ak) ^(H) F _(Ak) ^(H−1)(F _(Ak) H _(Ak) H _(Ak)^(H))⁻¹ =H _(Ak) ^(H)(H _(Ak) H _(Ak) ^(H))⁻¹ F _(Ak) ⁻¹

wherein the normalized channel matrix G_(k) has been decomposed intoG_(Ak) and G_(Bk) as per the channel matrix H_(k), and wherein F_(Ak)denotes a diagonal matrix comprising the diagonal coefficients of thediagonal matrix F_(k) corresponding to the N−M_(k) targeted lines.

Some power normalization is however required at transmit side throughpre-multiplication with the scaling matrix S_(Ak) in order to achievethe required transmit power, and thus the use of the nominal ornormalized channel matrix for the computation of the precoding matrixwill eventually yield the same effective precoding matrix.

Rectangular precoding is illustrated in FIG. 3.

N transceivers TU-C₁ to TU-C_(N) at network side supplies a downstreamtransmit vector u_(k) for every transmit DMT symbol period for furtherprecoding, transmission, reception and detection by N respectivetransceivers TU-R₁ to TU-R_(N) at subscriber side. The transmit vectoru_(k), comprising respective transmit frequency samples u_(1,k) tou_(N,k) after constellation mapping and scaling, is input to a precoderwith precoding matrix P_(k) to yield a precoded signal x_(k)=[x_(1,k) .. . x_(N,k)]^(T)=P_(k)u_(k) for further transmission over the respectivesubscriber lines L₁ to L_(N).

Let us assume for convenience that, at tone k, one line is being movedfrom the targeted set A_(k) to the supporting set B_(k) (i.e., M_(k)=1)in order to obtain a well-conditioned reduced channel matrix, and let usfurther assume that this supporting line is line L_(N). Thus nodownstream data is conveyed over line L_(N) at tone k, or equivalentlyu_(N,k)=0 (see crosshatched area in transmit vector u_(k)), andcorresponding transmit gain and bit loading are both set to zero. As aconsequence, the corresponding N^(th) column of the precoding matrixP_(k) is irrelevant as it does not play any role in signal precoding(see crosshatched area in precoding matrix P_(k)). The correspondingprecoding coefficients P_(1N) to P_(NN) are preferably (but notnecessarily) set to zero.

Yet, one or more off-diagonal coefficients of the N^(th) row of theprecoding matrix P_(k) are set to a value different from 0 (see boldenedcoefficients in precoding matrix P_(k)), meaning that crosstalkprecompensation signals keep on being transmitted over line L_(N) attone k despite tone k being disabled for direct data communication overline L_(N) (i.e., x_(N,k≠0) despite u_(N,k=0)). The effective precodingmatrix has thus a rectangular shape.

Next, the precoded vector x_(k) goes through the channel matrix H_(k),thereby yielding the receive vector y_(k)=[y_(1,k) . . . y_(N,k)]^(T)for reception and detection by the transceivers TU-R₁ to TU-R_(N). As nocommunication takes place over tone k for line L_(N), the transceiverTU-R_(N) discards the receive frequency sample y_(N,k) and thecorresponding N^(th) row of the channel matrix H_(k) is irrelevant (seecrosshatched area in channel matrix H_(k) and vector y_(k)).

A new rectangular N×(N−1) precoding matrix {tilde over (P)}_(Ak) iscomputed and enforced into the columns of the precoding matrix P_(k)corresponding to the targeted lines A_(k). The new rectangular precodingmatrix {tilde over (P)}_(Ak) makes an opportunistic use of the availabletransmit power over the supporting line L_(N) (on account of no datacommunication signal being sent on that line) for insertion over thatline of appropriately scaled and rotated replicas of the N−1communication signals u_(i,i≠N) (or a part thereof), and further forcoherent combining of these N−1 communication signals u_(i,i□N)traveling over the various propagation paths at the transceiversTU-R_(i,i≠N), which then undergo a substantial increase of their receivesignal power compared to full precoding (all lines being targeted withconsiderable signal down-scaling) or square tone suppression (one ormore lines being suppressed without any signal transmission over thesuppressed lines).

The data signal gain α_(i,k) over line L_(i) at tone k is given by:

$\begin{matrix}{{\alpha_{i,k} = {\sum\limits_{j = 1}^{N}{H_{{ij},k}P_{{ji},k}}}},} & (7)\end{matrix}$

and now comprises an additional term H_(iN,k)P_(Ni,k) on account of therectangular conditioning. This term will reinforce the power (ormagnitude) of the useful signal u_(i,k) provided the precodingcoefficient P_(Ni,k) is appropriately chosen.

The postcoding use case is very similar to the precoding use case.

Let us arrange the N×N [normalized] channel matrix asH_(k)=[H_(Ak)H_(Bk)], wherein H_(Ak) now denotes a reduced N×(N−M_(k))[normalized] channel matrix comprising the N−M_(k) columns of the[normalized] channel matrix H_(k) corresponding to the set of targetedlines A_(k) and all N rows, and H_(Bk) now denotes a reduced N×M_(k)[normalized] channel matrix comprising the M_(k) columns of the[normalized] channel matrix H_(k) corresponding to the set of supportinglines B_(k) and all N rows. In other words, the columns of the[normalized] channel matrix H_(k) have been re-arranged for thesupporting lines B_(k) to occupy the last M_(k) columns.

Let

$Q_{k} = \begin{bmatrix}Q_{AK} \\Q_{Bk}\end{bmatrix}$

denote the postcoding matrix used at tone k, with Q_(Ak) denoting areduced (N−M_(k))×N postcoding matrix comprising the N−M_(k) rows of thepostcoding matrix Q_(k) corresponding to the set of targeted lines A_(k)and all N columns, and Q_(Bk) denoting a reduced M_(k)×N postcodingmatrix comprising the M_(k) rows of the postcoding matrix Q_(k)corresponding to the set of supporting lines B_(k) and all N columns.

With zero-forcing postcoding and when all lines are targeted, we wouldstill have Q_(k)=H_(k) ⁻¹.

$\left. \begin{matrix}0 & S_{bk}\end{matrix} \right\rbrack$

still denotes the transmit gain scaling matrix. The diagonalcoefficients of the diagonal matrix S_(Bk) are set to zero as there areno communication signals transmitted over the supporting lines B_(k) attone k.

The VCU 130 is further configured, for respective ones of theill-configured tones used for upstream communication:

-   -   to determine a set A_(k) of targeted lines and a corresponding        set B_(k) of supporting lines to obtain a well-conditioned        reduced [normalized] channel matrix H_(Ak); and    -   to compute or recompute a rectangular postcoding matrix {tilde        over (Q)}_(Ak) for the targeted active lines A_(k) for which the        following three conditions hold:        -   a) The columns of {tilde over (Q)}_(Ak) corresponding to the            supporting lines B_(k) are not forced to zero, and thus the            signals that leak into the supporting lines B_(k) are            exploited for further enhancement of the data signal gains            over the targeted lines A_(k).        -   b) The columns of {tilde over (Q)}_(Ak) corresponding to the            targeted lines A_(k) are not the same as the corresponding            columns of the full postcoding matrix Q_(k) (i.e., when all            lines are targeted). This emphasizes that one does not just            take the columns of the full matrix inverse Q_(k)=H_(k) ⁻¹.        -   c) The (re)computed vectoring matrix {tilde over (Q)}_(Ak)            has a zero-forcing design and diagonalizes the overall            channel over the targeted lines A_(k):

$\begin{matrix}{{\left. \begin{matrix}\; & {\overset{\sim}{Q}{HS}} & {\overset{\sim}{Q}{HS}} \\{\,^{k}{{}_{}^{}{}_{}^{}}} & {{\overset{\sim}{Q}}_{Bk}H_{Ak}S_{Ak}} & {{\overset{\sim}{Q}}_{Bk}H_{Bk}S_{Bk}}\end{matrix} \right\rbrack = {\begin{bmatrix}{{\overset{\sim}{Q}}_{Ak}H_{Ak}S_{Ak}} & 0 \\{{\overset{\sim}{Q}}_{Bk}H_{Ak}S_{Ak}} & 0\end{bmatrix} = \begin{bmatrix}D_{Ak} & 0 \\X & 0\end{bmatrix}}},} & (8)\end{matrix}$

-   -   -    with D_(Ak) denoting a diagonal matrix. The coefficients of            the postcoding matrix {tilde over (Q)}_(Bk) are irrelevant            because the supporting lines B_(k) are not used for direct            data communication. These coefficients can be left            unchanged, or can be reset to zero.

One possible concrete postcoder computation is to use the Moore-Penrosepseudo-inverse for the reduced channel H_(Ak) as follows:

{tilde over (Q)} _(Ak)=(H _(Ak) ^(H) H _(Ak))⁻¹ H _(Ak) ^(H)  (9).

Other generalized inverses can serve as postcoder too, such as:

{tilde over (Q)} _(Ak)=(H _(Ak) ^(H) WH _(Ak))⁻¹ H _(Ak) ^(H) W  (10)

wherein W denotes a N×N diagonal matrix with real diagonal coefficients.

The same reasoning applies regarding the indistinct use of the channelmatrix or normalized channel matrix for the computation of thepostcoding matrix as per eq. (9) or (10): the corresponding postcodingmatrices will now only differ by left-multiplication with a diagonalmatrix, which diagonal matrix being anyhow compensated for by frequencyequalization at the receivers, which will re-normalize the power of thereceive samples before detection.

Rectangular postcoding is illustrated in FIG. 4.

N transceivers TU-R₁ to TU-R_(N) at subscriber side transmit respectivetransmit frequency samples u_(1,k) to u_(N,k) over the respectivesubscriber lines L₁ to L_(N) for further transmission, reception,postcoding and detection by N respective transceivers TU-C₁ to TU-C_(N)at network side. These transmit samples form a transmit vectoru_(k)=[u_(1,k) . . . u_(N,k)]^(T).

Let us again assume for convenience that, at tone k, one line is beingmoved from the targeted set A_(k) to the supporting set B_(k) (i.e.,M_(k)=1) in order to obtain a well-conditioned reduced channel matrix,and let us again further assume that this supporting line is line L_(N).Thus no upstream data is conveyed over line L_(N) at tone k, orequivalently u_(N,k)=0 (see crosshatched area in transmit vector u_(k)),and corresponding transmit gain and bit loading are both set to zero. Asa consequence, the corresponding N^(th) column of the channel matrixH_(k) is irrelevant (see crosshatched area in channel matrix H_(k)).

The receive vector y_(k)=[y_(1,k) . . . y_(N,k)]^(T)=H_(k)u_(k) goesthrough the postcoding matrix Q_(k) to yield the postcoded vectory′_(k)=[y′_(1,k) . . . y′_(N,k)]^(T)=Q_(k)y_(k). One or moreoff-diagonal coefficients of the N^(th) column of the postcoding matrixQ_(k) are set to a value different from 0 (see boldened coefficients inpostcoding matrix Q_(k)), meaning that the signal received from thesupporting line L_(N), which comprises all crosstalk signals from linesL₁ to L_(N−1) that have leaked into line L_(N), keep on being processedat tone k for further enhancement of the data signal gains over lines L₁to L_(N−1). The effective postcoding matrix has thus a rectangularshape.

A new rectangular (N−1)×N postcoding matrix {tilde over (Q)}_(Ak) iscomputed and enforced into the rows of the postcoding matrix Q_(k)corresponding to the targeted lines. The new rectangular postcodingmatrix {tilde over (Q)}_(Ak) makes an opportunistic use of the availablereceive power over the supporting line L_(N) (on account of no datacommunication signal being sent on that line) by appropriately scalingand rotating the N−1 crosstalk signals H_(Ni)u_(i,i≠N) (or a partthereof), and further for coherent combining of these N−1 crosstalksignals H_(Ni)u_(i,i≠N) at the transceivers TU-C_(i,i≠N), which thenundergo a substantial increase of the SNR before detection compared tofull postcoding (when all lines are targeted but with considerableincrease of the noise power because of the channel ill-conditioning) orsquare tone suppression (one or more lines being suppressed without anyreceive signal from the suppressed lines being exploited).

The data signal gain α_(i,k) over line L_(i) at tone k is given by:

$\begin{matrix}{{\alpha_{i,k} = {\sum\limits_{j = 1}^{N}{Q_{{ij},k}H_{{ji},k}}}},} & (11)\end{matrix}$

and now comprises an additional term Q_(iN,k)H_(Ni,k) on account of therectangular conditioning. This term will reinforce the strength of thedata signal u_(i,k) provided the postcoding coefficient Q_(iN,k) isappropriately chosen.

As no communication takes place over tone k for line L_(N) (seecrosshatched area in vector y′k), the transceiver TU-C_(N) discards thereceive frequency sample y′_(N,k) and the corresponding N^(th) row ofthe postcoding matrix Q_(k) is irrelevant (see crosshatched area inpostcoding matrix Q_(k)).

The performance of the proposed rectangular conditioning versus knownvectoring schemes are illustrated on FIGS. 6A and 6B.

FIG. 6A represents a comparison of the achievable data rates withprecoding based on the proposed rectangular conditioning (plot 501)versus precoding based on square tone suppression (plot 502) andprecoding based on full channel inverse when all lines in the system aretargeted (plot 503). Presently, the vectoring group comprises 48 lines.The lines are sorted according to their respective data rates, and thedata rates achieved with the respective precoding schemes are plottedfor the first 20 lines. As one can see, rectangular precoding clearlyoutperforms the other two precoding schemes.

In FIG. 6B, the real part of a precoding coefficient has been plottedversus frequency for the three considered precoding schemes. Again, thefrequency coherence for rectangular conditioning (plot 511) is clearlyhigher than for square tone suppression (plot 512) and full channelinverse (plot 513). The smoother variation of the precoder coefficientsacross frequency makes them easier to compress, resulting in lower costhardware.

It is to be noticed that the proposed rectangular conditioning does notneed to be restricted to ill-conditioned tones only, but can further beused at tones for which the full channel matrix is well-conditioned, forinstance in order to improve data rates over targeted bad-performinglines.

There is seen in FIG. 5 a flow chart for determining the sets oftargeted and supporting lines for successive tones.

When moving lines from the targeted set A_(k) to the supporting setB_(k) on a given tone, the overall data rates of the remaining targetedlines A_(k) are increased at the expense of the supporting lines B_(k).By choosing different subsets on different tones, advantageoustrade-offs can be made between lines to optimize desired objectives. Forexample, one objective may be to ensure that all lines achieve specifiedtarget rates.

Here, the goal is to adapt the targeted set to steer the line data ratestowards the specified target data rates. These target rates can be acommon minimum target data rate for all lines, or they can differ fromeach other in case particular lines get boosted target data rates forpremium service.

At step S00, the set of satisfied lines L₅ is initialized to the emptyset (L_(s)=Ø). For all tones k, the set of targeted lines A_(k) isinitialized to the set L (i.e., all vectored lines), and the set ofsupporting lines B_(k) is initialized to the empty set (i.e., M_(k)=0).A first tone index k=k₁ is selected, and the method starts.

At step S01, the set of targeted lines A_(k) is updated to the setL\L_(s) (i.e., the lines that have not yet satisfied their targetrates), and the set of supporting lines B_(k) is initialized to the setL_(s).

At next step S02, the VCU 130 computes a condition number ICN_(k) forthe reduced channel matrix H_(Ak).

At step S03, the VCU 130 determines whether the [reduced] channel matrixH_(Ak) is ill-conditioned by comparing the condition number ICN_(k)versus some threshold.

If the condition number ICN_(k) is greater than the threshold, then the[reduced] channel matrix H_(Ak) is expected to be ill-conditioned, andone or more subscriber lines should be removed from the targeted setA_(k) for that tone. Consequently, at step S04, a line is selected andmoved from the set of targeted lines A_(k) to the set of supportinglines B_(k), and the VCU 130 re-iterates through the steps S02 and S03till the [reduced] channel matrix H_(Ak) is no longer ill-conditioned.This procedure is guaranteed to stop before A_(k) is empty, because areduced channel matrix consisting of a single row or column is alwayswell-conditioned.

When the condition number ICN_(k) is lower than the given threshold,then the [reduced] channel matrix H_(Ak) is not or is no-longerill-conditioned, and no or no more lines need to be removed from thetargeted set A_(k).

The VCU 130 goes to next step S05, and configures a new rectangularvectoring matrix {tilde over (P)}_(Ak) or {tilde over (Q)}_(Ak) as perthe present invention.

At step S06, the VCU 130 updates respective line metrics LM_(n) for alllines L₁ to L_(N) based on the configured set of targeted lines A_(k)and set of supporting lines B_(k), and on the configured vectoringmatrix {tilde over (P)}_(Ak) or {tilde over (Q)}_(Ak). The line metricmay refer for instance to an aggregate achievable data rate or anaggregate transmit power across all the tones that have been configuredso far.

For the computation of the aggregate achievable data rates, anestimation of the achievable bit loadings for the respective tones needsto be carried out. This estimation can be based on actual errormeasurements at the receivers after the new vectoring matrix {tilde over(P)}_(Ak) or {tilde over (Q)}_(Ak) has been enforced, or can be based onan estimation of the data signal gains based on the configured vectoringmatrix and an estimate of the channel matrix H. The bit loadingcomputation is typically based on the Shannon capacity formula, andincludes a given SNR gap to account for the particular coding andmodulation schemes being used, and possibly a given SNR margin to absorbnoise fluctuations if any.

At step S07, each of the updated line metrics is tested against arespective target metric. If a current line metric LM_(n) for aparticular line L_(n) is greater than a respective target metric LMT_(n)to be achieved over that line, then at step S08 the line L_(n) is addedto the set of satisfied lines L_(s). This means that L_(n) will bepre-assigned to the set of supporting lines B_(k) for subsequent k,thereby giving precedence to the lines that did not yet achieve theirrespective target metric for the next tone iterations.

If the respective target metrics are met over all the lines L₁ to L_(N),then this pre-assignment is no longer necessary, and the set L_(s) canbe re-initialized to the empty set.

Last, at step S09, a new tone index k is selected, and one re-iteratesfrom step S01 onwards with the new selected tone index k till all toneshave been processed. The tones can be processed in a deterministicorder, such as increasing or decreasing tone index, or can be processedin a random or pseudo-random order.

The targeted set and the supporting set may be reinitializedoccasionally (e.g., every 200^(th) tone), for instance in order toprevent a line that contributes to the ill-conditioning on a given tonefrom being removed for all subsequent tones.

FIG. 6C represents a plot of the data rates achieved over respectiveones of a group of vectored lines. Line 4 is a line with a bad contact,causing low direct gain and high crosstalk. Plot 521 corresponds toprecoding with full channel inverse when all lines are targeted. In thiscase line 4 obtains a very low data rate. Plot 522 corresponds to theproposed method with target rates configured at 1 Gbps for all lines. Itcan be seen that the proposed scheme achieves the target rate for alllines, including the line with the bad contact.

In an alternative embodiment, the VCU 130 does not wait for a metrictarget to be met before pre-assigning a line to the set of supportinglines for subsequent tone iterations. Instead, the aggregate data ratesare tracked through the successive tone iterations, and if some linesare allocated much more data rates than others, then they are removedfrom the set of targeted lines for one or more subsequent toneiterations till the data rates are again appropriately balanced.

For instance, the lines can be sorted according to their respective datarates, and the ratio or difference between the maximum and minimum datarates can be computed and compared to some given threshold for decidingwhether the line with the maximum data rate shall be pre-assigned to theset of supporting lines for one or more subsequent tone iterations.

This embodiment is further advantageous in that data rate arecontinuously rebalanced while iterating through the steps of the method.

Once a given line achieves its metric target, then the first algorithmmay kick in and that line may be pre-assigned to the set of supportinglines for subsequent tone iterations.

It is to be noticed that the term ‘comprising’ should not be interpretedas being restricted to the means listed thereafter. Thus, the scope ofthe expression ‘a device comprising means A and B’ should not be limitedto devices consisting only of components A and B. It means that withrespect to the present invention, the relevant components of the deviceare A and B.

It is to be further noticed that the term ‘coupled’ should not beinterpreted as being restricted to direct connections only. Thus, thescope of the expression ‘a device A coupled to a device B’ should not belimited to devices or systems wherein an output of device A is directlyconnected to an input of device B, and/or vice-versa. It means thatthere exists a path between an output of A and an input of B, and/orvice-versa, which may be a path including other devices or means.

The description and drawings merely illustrate the principles of theinvention. It will thus be appreciated that those skilled in the artwill be able to devise various arrangements that, although notexplicitly described or shown herein, embody the principles of theinvention. Furthermore, all examples recited herein are principallyintended expressly to be only for pedagogical purposes to aid the readerin understanding the principles of the invention and the conceptscontributed by the inventor(s) to furthering the art, and are to beconstrued as being without limitation to such specifically recitedexamples and conditions. Moreover, all statements herein recitingprinciples, aspects, and embodiments of the invention, as well asspecific examples thereof, are intended to encompass equivalentsthereof.

The functions of the various elements shown in the figures may beprovided through the use of dedicated hardware as well as hardwarecapable of executing software in association with appropriate software.When provided by a processor, the functions may be provided by a singlededicated processor, by a single shared processor, or by a plurality ofindividual processors, some of which may be shared. Moreover, aprocessor should not be construed to refer exclusively to hardwarecapable of executing software, and may implicitly include, withoutlimitation, Digital signal Processor (DSP) hardware, network processor,Application specific Integrated circuit (ASIC), Field Programmable GateArray (FPGA), etc. Other hardware, conventional and/or custom, such asRead Only Memory (ROM), Random Access Memory (RAM), and non volatilestorage, may also be included.

1.-15. (canceled)
 16. A vectoring controller for configuring a vectoringprocessor that jointly processes Discrete Multi-Tone DMT communicationsignals to be transmitted over, respectively received from, a pluralityof N subscriber lines according to a vectoring matrix, and adapted, forgiven ones of a plurality of tones: to enable the given tone for directdata communication over a first set of N−Mk targeted lines out of the Nsubscriber lines, and to disable the given tone for direct datacommunication over a second disjoint set of M_(k) supporting lines outof the N subscriber lines, M_(k) denoting a nonnull positive integer, toconfigure the vectoring matrix to use an available transmit power,respectively an available receive power, at the given tone over thesecond set of M_(k) supporting lines for enhancement of data signalgains at the given tone over the first set of N−M_(k) targeted lines,wherein the vectoring controller is further adapted to distributetargeted and supporting roles across the N subscriber lines whileiterating through the plurality of tones in sequence in order to achieverespective target data rates over the N subscriber lines, and whereinthe vectoring controller is further adapted, during the respectiveiterations, to update respective data rates achievable over the Nsubscriber lines given the so-enabled and so-disabled tones and thevectoring matrices configured so far, and to determine the first andsecond sets of lines based on the updated data rates.
 17. A vectoringcontroller according to claim 16, wherein the vectoring controller isfurther adapted to assign at least one subscriber line of the pluralityof N subscriber lines, whose updated data rate exceeds a target datarate, to the second set of M_(k) supporting lines for at least onesubsequent iteration.
 18. A vectoring controller (130) according toclaim 16, wherein the vectoring controller is further adapted to assignat least one subscriber line of the N subscriber lines, whose updateddata rate exceeds by a given margin at least one further updated datarate of at least one further subscriber line of the N subscriber lines,to the second set of M_(k) supporting lines for at least one subsequentiteration.
 19. A vectoring controller according to claim 16, wherein theconfigured vectoring matrix is a rectangular N×(N−M_(k)) precodingmatrix with at least one non-null off-diagonal precoding coefficient forthe respective M_(k) matrix rows corresponding to the second set ofM_(k) supporting lines.
 20. A vectoring controller according to claim19, wherein the configured rectangular vectoring matrix is a generalizedinverse matrix of a (N−M_(k))×N reduced channel matrix comprisingfar-end coupling coefficients from the N subscriber lines into the firstset of N−M_(k) targeted lines.
 21. A vectoring controller according toclaim 20, wherein the generalized inverse matrix is a Moore-Penrosepseudo-inverse of the (N−M_(k))×N reduced channel matrix.
 22. Avectoring controller according to claim 16, wherein the configuredvectoring matrix is a rectangular (N−M_(k))×N postcoding matrix with atleast one non-null off-diagonal postcoding coefficient for therespective M_(k) matrix columns corresponding to the second set of Mksupporting lines.
 23. A vectoring controller according to claim 22,wherein the configured rectangular vectoring matrix is a generalizedinverse matrix of a N×(N−M_(k)) reduced channel matrix comprisingfar-end coupling coefficients from the first set of N−M_(k) targetedlines into the N subscriber lines.
 24. A vectoring controller accordingto claim 23, wherein the generalized inverse matrix is a Moore-Penrosepseudo-inverse of the N×(N−M_(k)) reduced channel matrix.
 25. An accessnode for providing broadband communication services to subscribers, andcomprising a vectoring controller according to claim
 16. 26. A methodfor configuring a vectoring processor that jointly processes DiscreteMulti-Tone DMT communication signals to be transmitted over,respectively received from, a plurality of N subscriber lines accordingto a vectoring matrix, and comprising, for given ones of a plurality oftones: enabling the given tone for direct data communication over afirst set of N−M_(k) targeted lines out of the N subscriber lines, anddisabling the given tone for direct data communication over a seconddisjoint set of M_(k) supporting lines out of the N subscriber lines,M_(k) denoting a nonnull positive integer, configuring the vectoringmatrix to use an available transmit power, respectively an availablereceive power, at the given tone over the second set of M_(k) supportinglines for enhancement of data signal gains at the given tone over thefirst set of N−M_(k) targeted lines, wherein the method furthercomprises distributing targeted and supporting roles across the Nsubscriber lines while iterating through the plurality of tones insequence in order to achieve respective target data rates over the Nsubscriber lines, and wherein the method further comprises, during therespective iterations, updating respective data rates achievable overthe N subscriber lines given the so-enabled and so-disabled tones andthe vectoring matrices configured so far, and determining the first andsecond sets of lines based on the updated data rates.